Chapter 3. Vectors and Coordinate Systems Our universe has three dimensions, so some quantities also need a direction for a full description. For example, wind has both a speed and a direction; hence the motion of the wind is described by a vector. Chapter Goal: To learn how vectors are represented and used.

Chapter 3. Vectors and Coordinate Systems Topics: Vectors Properties of Vectors Coordinate Systems and Vector Components Vector Algebra

Chapter 3. Reading Quizzes

What is a vector? A quantity having both size and direction The rate of change of velocity A number defined by an angle and a magnitude The difference between initial and final displacement None of the above Answer: A

What is a vector? A quantity having both size and direction The rate of change of velocity A number defined by an angle and a magnitude The difference between initial and final displacement None of the above IG3.1

What is the name of the quantity represented as ? ^ Eye-hat Invariant magnitude Integral of motion Unit vector in x-direction Length of the horizontal axis Answer: C

What is the name of the quantity represented as ? ^ Eye-hat Invariant magnitude Integral of motion Unit vector in x-direction Length of the horizontal axis IG3.2

This chapter shows how vectors can be added using graphical addition. algebraic addition. numerical addition. both A and B. both A and C. Answer: D

This chapter shows how vectors can be added using graphical addition. algebraic addition. numerical addition. both A and B. both A and C. IG3.3

To decompose a vector means to break it into several smaller vectors. to break it apart into scalars. to break it into pieces parallel to the axes. to place it at the origin. This topic was not discussed in Chapter 3. Answer: C

To decompose a vector means to break it into several smaller vectors. to break it apart into scalars. to break it into pieces parallel to the axes. to place it at the origin. This topic was not discussed in Chapter 3. IG3.4

Chapter 3. Basic Content and Examples

EXAMPLE 3.2 Velocity and displacement QUESTION:

EXAMPLE 3.2 Velocity and displacement

EXAMPLE 3.2 Velocity and displacement

EXAMPLE 3.2 Velocity and displacement

EXAMPLE 3.2 Velocity and displacement

Tactics: Determining the components of a vector

EXAMPLE 3.3 Finding the components of an acceleration vector

EXAMPLE 3.3 Finding the components of an acceleration vector

EXAMPLE 3.3 Finding the components of an acceleration vector

EXAMPLE 3.3 Finding the components of an acceleration vector

EXAMPLE 3.5 Run rabbit run!

EXAMPLE 3.5 Run rabbit run!

EXAMPLE 3.5 Run rabbit run!

EXAMPLE 3.5 Run rabbit run!

EXAMPLE 3.7 Finding the force perpendicular to a surface

EXAMPLE 3.7 Finding the force perpendicular to a surface

EXAMPLE 3.7 Finding the force perpendicular to a surface

Chapter 3. Summary Slides

Important Concepts

Important Concepts

Using Vectors

Using Vectors

Using Vectors

Using Vectors

Chapter 3. Clicker Questions

Which figure shows ? Answer C

Which figure shows ? STT3.1

Which figure shows 2 − ? Answer A

Which figure shows 2 − ? STT3.2

What are the x- and y-components Cx and Cy of vector ? Cx = 1 cm, Cy = –1 cm Cx = –3 cm, Cy = 1 cm Cx = –2 cm, Cy = 1 cm Cx = –4 cm, Cy = 2 cm Cx = –3 cm, Cy = –1 cm Answer D

What are the x- and y-components Cx and Cy of vector ? Cx = 1 cm, Cy = –1 cm Cx = –3 cm, Cy = 1 cm Cx = –2 cm, Cy = 1 cm Cx = –4 cm, Cy = 2 cm Cx = –3 cm, Cy = –1 cm STT3.3

Angle φ that specifies the direction of is given by tan–1(Cy /Cx) tan–1(Cx /|Cy|) tan–1(Cy /|Cx|) tan–1(Cx /Cy) tan–1(|Cx |/|Cy|) Answer D

Angle φ that specifies the direction of is given by tan–1(Cy /Cx) tan–1(Cx /|Cy|) tan–1(Cy /|Cx|) tan–1(Cx /Cy) tan–1(|Cx |/|Cy|) STT3.4